The sharing buttons configured in the JFBConnect > Social area is for the bottom of content articles. The behavior you're describing sounds correct.
However, it sounds like you're looking for the floating module with the share buttons at the bottom of the page like on sourcecoast.com. To do this, please use the JFBCSocialShare module. To get you started, the following are the parameter values we use for our site:
Layout: Button Count
Orientation: Horizontal
Position: Float
Margin: 5px
Padding: 5px 0 0 5px
Background: #fff
Float from Top: 3000 (this puts it at the bottom of the screen)
Float from Left: 3000 (this puts in on the right side)
In the Facebook section, we have:
Show Like: Yes
Width: 85
Height: 20
If this is not what you're looking for, please give further details. You can also send a private message to me using the envelope icon under my avatar.
-Melissa